The purpose of this work is to develop non-parametric hypothesis tests for use in general situations. The tests are developed for right-, left-, or interval-censored data as well as for repeated measures data using permutation methods. We estimate a functional of the hyper-distributions of the treatment groups using U-statistic methods and estimated distribution functions for individuals. Several different types of tests may be formed depending on the choice of functional, motivated by the type of treatment difference we wish to highlight, or the choice of estimated distribution function, motivated by the type of data. When a Mann-Whitney functional is used with repeated measures data, we obtain a new rank invariant test analogous to an ANOVA test. When a difference in means functional is used with censored data, we obtain a new test which generalizes the permutation t-test to censored data. This new methodology is useful when standard assumptions (for example, proportional hazards or proportional odds) do not hold. The methodology is being extended to create stratified tests for censored data. During 1997, one paper has been accepted for publication on this methodology and one is almost ready for submission. A related paper was submitted that compares different scores tests for interval censored data. These tests have identical scores to some related permutation tests using the above method.